EAN: 9783642217180

NONLINEAR PDES AND APPLICATIONS - STEFANO BIANC...

This volume collects the notes of the CIME course Nonlinear PDE's and applications held in
Cetraro (Italy) on June 23-28  2008. It consists of four series of lectures  delivered by
Stefano Bianchini (SISSA  Trieste)  Eric A. Carlen (Rutgers University)  Alexander Mielke (WIAS
Berlin)  and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview
of far-reaching findings and exciting new developments concerning  in particular  optimal
transport theory  nonlinear evolution equations  functional inequalities  and differential
geometry. A sampling of the main topics considered here includes optimal transport 
Hamilton-Jacobi equations  Riemannian geometry  and their links with sharp geometric functional
inequalities  variational methods for studying nonlinear evolution equations and their scaling
properties  and the metric energetic theory of gradient flows and of rate-independent evolution
problems. The book explores the fundamental connections between all of these topics and points
to new research directions in contributions by leading experts in these fields.

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